The National Hurricane Center says Irma made landfall on the Camaguey Archipelago of Cuba late Friday and has maximum sustained winds of 160 miles per hour.
The U.S. National Hurricane Center says the storm is now centered about 145 miles south of the Gulf coast city of Tampico in a mountainous region dotted with small towns.
It says the storm was centered about 130 miles (210 kilometers) north of the port of Veracruz and it seems headed for strike early Saturday in an area known as the Emerald Coast that is popular with Mexican tourists.
Forecasters have predicted damaging winds, drenching rains and a risky storm surge from the Gulf of Mexico.
Mexico is dealing with the aftermath of a huge quake that struck on Thursday night, and President Enrique Pena Nieto said on Friday that Katia could be especially risky in hillsides rocked by the magnitude 8.1 tremor. "Some strengthening is forecast during the next day or so and Katia could be near major hurricane strength at landfall".
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Meanwhile, Mexico is dealing with the aftermath of a powerful quake on Thursday night.
Mexican emergency workers are also scrambling to respond to an 8.1-magnitude natural disaster that struck off the country's southern Pacific coast late Thursday, killing at least 61 people.
As Katia rapidly weakened, Hurricane Jose continued to gather strength far out in the Atlantic.
Mexico's national emergency services said this week that Katia was worrying because it is very slow-moving and could dump a lot of rain on areas that have been saturated in recent weeks. It was expected to gain some strength but the effects of Irma were seen eventually weakening that storm.
By Saturday afternoon, the hurricane is expected to be downgraded to a tropical storm. Millions of Florida residents were ordered to evacuate after the storm killed 21 people in the eastern Caribbean and left catastrophic destruction in its wake.